Vanishing of Topological Invariants For Unnormalized Schatten p multiplicative Maps

2025/09/30 by Glebe, Forrest
#FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2509.25869

Abstract

A result of Dadarlat shows that nonzero even rational cohomology obstructs the matricial stability of many discrete groups. In the author's previous work, 2-cohomology is used to argue that certain groups are not stable in unnormalized Schatten p-norms for p > 1, although 2-cohomology is known not to obstruct stability in the unnormalized 2-norm in general. The main result of this paper demonstrates that we should not expect 2k cohomology to obstruct in the unnormalized Schatten p-norm for p≤ k, because the invariant in Dadarlat's argument vanishes for maps that are asymptotically multiplicative in the Schatten p-norm.

Citations

• On Chern classes of almost representations
• Central extensions and almost representations
• A Cup Product Obstruction to Frobenius Stability
• Stability and instability of lattices in semisimple groups
• Frobenius Non-Stability of Nilpotent Groups
• Obstructions to matricial stability of discrete groups and almost flat\n K-theory
• Stability, cohomology vanishing, and non-approximable groups
• Almost flat K-theory of classifying spaces
• Groups acting properly on "bolic" spaces and the Novikov conjecture

Related

• A Constructive Proof that Many Groups with Non-Torsion 2-Cohomology are Not Matricially Stable
• Obstructions to matricial stability of discrete groups and almost flat\n K-theory
• A Cup Product Obstruction to Frobenius Stability
• Non-stable groups
• Stability, cohomology vanishing, and non-approximable groups